I would say core 90s is 1992-1997. :)

1992 simply had too many remnants of the '80s still lingering or dying down. It was probably the last calendar year where it'd be easy to mistake a lot of things for being the late '80s, simply because new trends hadn't completely taken over yet.

Core '90s, that defined as being the time that was most distinctive from the '80s/'00s, would be something like mid 1993 to mid 1997. You had Clinton as president, early internet, grunge/post-grunge, gangsta rap, a new influx of TV shows and video games, and a generally distinctive style.

I agree with you NewMedalz. Commercials with late '80s copyright dates or releases on them were still occasionally seen though in 1992, such as the "Tone It Up!" soap ad from 1987, the 1988 Centrum commercial, the 1987 100% Colombian Coffee ad (even seen as late as 1995), and Kris Kross is more akin to Golden Age as opposed to Gangsta Hip Hop. The last remant of the Cold War, Czechoslovakia was still joined. Even the NES was still selling its original style as the top loader wouldn't come out until Clinton was in office, and most schools still used Apple II-series computers. Bill Cosby, The Golden Girls, Growing Pains, Who's The Boss?, Full House with white opening credits, the original MacGyver, and Night Court were still on network TV up through summer reruns, and the final episodes of Double Dare with Marc Summers were produced. Wilson Phillips, New Kids On The Block, and even Rick Astley had their final hit songs. Yes, grunge was quite popular, but it wasn't yet Hollywood mainstream and more people still had a Game Boy than a Sega Genesis. 1992 is the last "early '90s" year for those reasons.

1993 though had Clinton, grunge now acceptable in Peoria, the launch of MTV.com, Beavis and Butthead showcasing that the most popular things about the channel aren't about music, the first fifth-generation gaming system release (Jaguar), and Super Sentai now in a westernized version. The graphic design in advertising also seemed to begin its edgier shift that continues to leave its legacy well into the 21st century, including features such as swooshes, more rounded, "curvy" fonts, smaller type on car advertising, and more. This continued until the Y2K style started to kick in towards the end of 1998, although there were hints of it in since around the end of 1996, the end of the "core '90s". 

I don't think there is such a thing as a "core" when it comes to the '90s. Everything just changed so much throughout the decade that you can hardly say any one stretch of time stood for a definitive characterization of the time. The early '90s were grungy, the mid-'90s began the "Friends" era of Gen X culture, and the late '90s/early '00s were swamped with boy and girl bands.